Time dependent hazard ratio estimation using instrumental variables without conditioning on an omitted covariate

Abstract Background Estimation that employs instrumental variables (IV) can reduce or eliminate bias due to confounding. In observational studies, instruments result from natural experiments such as the effect of clinician preference geographic distance on treatment selection. randomized studies randomization indicator is typically a valid instrument, especially if study blinded, e.g. no placebo effect. via highly developed field for linear models but use in time-to-event analysis far established. Various IV-based estimators hazard ratio (HR) Cox’s regression have been proposed. Methods We extend IV based estimation model beyond proportionality hazards, and address log-linear time dependent piecewise constant HR. estimate marginal time-dependent unlike other approaches conditional omitted covariates. estimating equations motivated by Martingale representations resemble partial likelihood score statistic. conducted simulations include copulas generate potential times-to-event given structural are compare our approach estimator, two approaches. apply it vascular interventions. Results The method performs well stepwise ratio, illustrates some increases moves away unity (the value underlies null hypothesis). It compares when constant. also where variable exist. Conclusion we propose using an perform simulations. encourage procedure unmeasured confounding concern suitable exists.